報(bào)告題目：The CP-matrix completion problem
報(bào)告時(shí)間：2017年9月8日（周五）9:00-10:00
報(bào)告地點(diǎn)：西教五416（理學(xué)院）
報(bào)告人：范金燕
報(bào)告人簡(jiǎn)介：
范金燕，上海交通大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授。2002年在中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院獲博士學(xué)位。先后訪(fǎng)問(wèn)英國(guó)劍橋大學(xué)和美國(guó)加州大學(xué)圣迭戈分校。主要從事非線(xiàn)性最優(yōu)化的理論和方法研究，在非線(xiàn)性方程組的數(shù)值解法和完全正優(yōu)化方面取得了一系列重要的成果，提出了非線(xiàn)性方程組的高階Levenberg-Marquardt方法和信賴(lài)域半徑趨于零的信賴(lài)域方法，解決了矩陣領(lǐng)域中的完全正填充問(wèn)題和完全正分解問(wèn)題。所指導(dǎo)博士獲2016年全國(guó)博士后創(chuàng)新人才計(jì)劃。2017年獲第十三屆中國(guó)青年女科學(xué)家獎(jiǎng)。
報(bào)告摘要：
A symmetric matrix $C$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $C="BB^T$." The CP-completion problem is to study whether we can assign values to the missing entries of a partial matrix such that the completed matrix is completely positive. In this talk, we propose a semidefinite algorithm for solving general CP-completion problems, and study its properties. When all the diagonal entries are given, the algorithm can give a certificate if a partial matrix is not CP-completable, and it almost always gives a CP-completion if it is CP-completable. When diagonal entries are partially given, similar properties hold. Computational experiments are also presented to show how CP-completion problems can be solved.
